Differential refractometers are widely used as detectors for the chromatographic analysis of a broad range of chemical compounds including polymers, pharmaceuticals, and food products. Concentrations of solutes of 10.sup.-6 to 10.sup.-8 g/ml are commonly detected. Differential refractometers produce a signal which is proportional to the difference of the refractive index between at sample and a reference solution. The reference is usually a pure solvent. In the limit of vanishingly small solute concentration dc, the variation of the sample refractive index dn is defined to be dn/dc. This value is dependent on both the dissolved compound and the solvent, and must be determined in order to relate the instrument refractive index change to the instantaneous solute concentration. Once the value of dn/dc is known at a particular wavelength for a particular compound and solvent, the refractometer can be used as an absolute concentration detector. If the instrument response is .DELTA.n, then the solute concentration change above that of the pure solvent .DELTA.c is related simply by .DELTA.c=.DELTA.n/(dn/dc)+O(.DELTA.n.sup.2) .
During the past 20 years, there has been increased interest in the use of light scattering to measure molar mass during chromatographic analysis. The first combination of an on-line chromatographic separation combined with a refractive index detector and light scattering detector was preformed in 1974 by Ouano and Kaye (J. Poly. Sci. A-1, volume 12, page 1152). The amount of light scattered into small scattering angles is directly proportional to the product of molar mass; times concentration. Thus by dividing the light scattering signal by the concentration signal, the molar mass of each eluting fraction may be determined. Since the refractive index increment, dn/dc, also appears in the light scattering equations, it should be measured at the same wavelength as the light scattering measurement. There has always been a need for an accurate refractometer that is sensitive enough to serve as a chromatographic detector, and has a sufficiently wide range to measure dn/dc at both convenient laboratory concentrations and the very low concentrations associated with HPLC separations. Unfortunately, for reversed phase chromatography, the refractive index change of the solvent gradient itself will often drive the differential refractive index detector off scale. For many types of HPLC separations, the concentration variation among the separated peaks is so great that for some peaks the refractive index responses saturate the RI detector while for others, the response may be so low as to be undetectable. Therefore there is a need for a refractometer with great sensitivity and great dynamic range. Most refractometers increase the dynamic range at the expense of decreased sensitivity or vice versa.
Most of the existing commercial refractometers are based directly on Snell's Law of Refraction, EQU n.sub.1 sin(.theta..sub.1)=n.sub.2 sin(.theta..sub.2) (1)
which relates the refractive index of two materials, with refractive index n.sub.1 and n.sub.2, to the refraction of a light beam striking the interface between the materials. The usual instrument design forms the sample into a prism to deflect a light beam, and then uses an opposed prism of reference material to refract it back. Any net deflection of the beam then indicates the presence of the sample material.
Another type of refractometer measures the intensity of light reflected from the liquid-glass interface of a sample cell relative to a beam reflected from the liquid-glass interface of the reference fluid. Based on Fresnel's laws of reflection at such an interface, the incident beams are normally oriented to strike the interfaces close to the critical angle The reflected beams are then focused onto the surface of a dual element photodetector for subsequent amplification and recording. Such refractometers also have a rather limited linear range. Although intensity based refractive index detectors are available, the deflection type still remains the most common.
An interferometric refractometer has long been considered the ideal device by which refractive index changes may be measured. The interferometer compares the optical phase shift of equal length light beams in the sample and reference cells. The phase difference in radians is .phi. where: EQU .phi.=2.pi.(n.sub.1 -n.sub.2)L/.lambda. (2)
L is the length of the cell and .lambda. is the wavelength of light in vacuum. This measurement is a linear function of the refractive index difference, and the calibration constant is the same for any solvent refractive index. The interferometric refractometer produces a signal based upon the interference of two beams which have traversed separate paths corresponding to a reference material and a sample material. As long as the contrast between these combining beams remains high, the interferometer will present a series of fringes corresponding to a generally enhanced range of refractive indices measurable. Because of the broad operating range associated with the multi-pathlengths and the inherent sensitivity of the interferometric measurement, such interferometric refractometers have been developed to overcome many of the disadvantages of the deflection method.
A practical interferometric refractometer is the "polarization interferometer" or "wave shearing interferometer". This device is referred to as "Smith's Polarization Interferometer" in some texts, and it was first commercially produced in Sweden by Biofoc AB in the 1970's. During the 1980's it was developed and sold by the Swedish company Tecator under the trade name Optilab. Some elements of its flow cell design are described in Silverbage's U.S. Pat. No. 4,229,105. Since about 1992, the instruments have been manufactured by Wyatt Technology Corporation of Santa Barbara Calif. who have improved the design further. In the discussion below, we refer to the differential refractometer based on Smith's Polarization Interferometer as the "Optilab".
The Optilab differential refractometer uses a tungsten light source whose collimated beam is linearly polarized at 45 degrees to the optical axes of a Wollaston prism which then divides it into two orthogonal linearly polarized beams. The diverging beams are made parallel by a lens. The vertically polarized beam passes through the sample cell while the horizontally polarized beam passes through a parallel reference cell. The transmitted beams are then recombined by another lens and a second Wollaston prism. A quarter wave retarder is then used to convert each of the linearly polarized components into circularly polarized light. The vertically polarized beam becomes circularly polarized clockwise and the horizontally polarized beam becomes circularly polarized counterclockwise. The resulting superposition of counter-rotating circular waves add to produce an elliptically polarized beam. Ideally, the minor axis is zero and the beam is linearly polarized. In practice, the quarter waveplate shift is not exactly 90.degree.. The rotation of the major axis of the ellipse is measured. The angle of the axis rotates relative to the initial 45.degree. linearly polarized beam at half the phase shift introduced by the difference between the sample and reference cells, i.e. EQU .theta.=.phi./2, (3)
where .theta. is the angle of the major axial polarization and .phi. is given by Eq. (2).
This remarkable result means that the optical phase shift of the interferometer produces a physically measurable angle of polarization. In the Optilab instrument, the elliptically polarized beam is transmitted through a polarization analyzer, a narrow band interference filter, and then on to a silicon photodiode detector. In the ideal, linearly polarized case, assuming the analyzer angle is zero, the resulting signal intensity I varies sinusoidally as: EQU I=I.sub.0 cos.sup.2 .theta.=1/2I.sub.0 [1+cos .phi.]. (4)
The reference intensity scale I.sub.0, can be established by physically rotating the analyzer to measure the maximum and minimum intensity values.
The most linear part of the signal is near I=1/2I.sub.0, where cos (.phi.)=0. Shifting the signal intensity axis up to 1/2I.sub.0, and the phase axis 90.degree. by rotating the analyzer, the shifted phase angle .phi.'=.phi.+.pi./2. Define the shifted intensity I.sub.S =2I-I.sub.0 so that one has EQU I.sub.S =I.sub.0 sin .phi.'=I.sub.0 .phi.'+O(.phi.'.sup.3) (5) EQU .thrfore.I.sub.S /I.sub.0 .apprxeq.I.sub.0 2.pi.(n.sub.1 -n.sub.2)L/.lambda.(6)
for small values of .phi.'.
At the limit of its sensitivity, the Optilab provides a linear signal proportional to the refractive index difference, with sensitivity determined by cell length L, optical wavelength in vacuum .lambda., and a simple intensity normalization based on rotating the polarization analyzer to determine I.sub.0. A later model, the Wyatt Optilab-DSP, uses a microprocessor to compute the arcsine for Eq. (5) and thus extends the linear range slightly. The microprocessor also controls the motion of the polarization analyzer.
Optilab manufacturers have met the need for both highly sensitive chromatographic measurements and wide range dn/dc measurements by offering several cells of different lengths, L. Normally dn/dc, measurements are made with a 0.2 mm long cell, and chromatographic measurements use cells or 1 or 10 mm in length. The cells are expensive and require some re-plumbing to change.
Wavelengths corresponding to lasers used in light scattering instruments, such as the DAWN-DSP multiangle light scattering photometer manufactured by Wyatt Technology Corporation of Santa Barbara Calif., include 690 nm, 633 nm, 514 nm, and 488 nm. Other wavelengths are easily provided by changing the internal interference filter and quarter wave plate to the desired wavelength and adjusting the optics accordingly.
It is possible to use the direct Optilab signal to measure very large changes in refractive index, providing that one can follow the signal through the many fringes that could occur, computing the arcsine as one goes. This method is ambiguous at the peaks of the refractive index signal, since there is no certain indication that the slope of the signal has reversed. Some workers such as Van Hook at the University of Tennessee have used several instruments with different wavelengths of light to help resolve the ambiguity. Details may be found in the paper by M. Smith and W. A. Van Hook in Z. Naturforschung, volume 44A, pages 371 to 375 (1989). The key to using the Optilab at a single wavelength for measuring large refractive index changes is having the ability to measure the rotating angle of polarization of the exiting beam over many rotations. Of course this is a familiar problem in many types of interferometric instruments, and a familiar solution is to use a "quadrature" signal, a cosine to accompany the sine, and thus resolve the ambiguity of direction. Ideally, we seek a refractometer of the Optilab type that is comprised of a single high sensitivity cell, such a the 10 mm cell, that can be used both for high sensitivity chromatography detection, and for low sensitivity dn/dc measurements, and can be used also for gradient reversed phase chromatography where the refractive index of the mobile phase solvent varies over a wide range during the chromatographic separation. Such an "Extended Range Optilab" would meet the need for chromatography detection, gradient chromatography detection and dn/dc measurement in a single instrument.